We prove Theorem REF  (see also Theorem REF ) following the same approach as in [1]} (see also [2]}), based on Kashiwara's index theorem for constructible complexes of sheaves (cf. [3]}), together with (semi-)positivity results for nef (resp., ample) bundles (cf. [4]}, [5]}). It is well-known that if \(X\)  has non-positive (resp., negative) sectional curvature, then \(T^*X\)  is nef (resp., ample); see, e.g., [4]} or [2]}. And, as already mentioned, it was conjectured in [1]} that aspherical complex projective manifolds have nef cotangent bundles.
